6. LEARNING COMPETENCIES:
At the end of the discussion, students will be able to:
a) define an ellipse
b) graph an ellipse
c) determine the standard equation of a ellipse given center, major axis,
minor axis and axis of symmetry.
d) determine the center, major vertices, minor vertices, foci, latera recta,
directrices and directrix given the equation of a ellipse.
8. DEFINITION OF TERMS
Ellipse
It is a set of all points on a plane whose sum of distances from two
fixed points called foci is constant.
Foci
It is the two fixed points of the ellipse and is denoted by F and F’.
11. Properties of Ellipse
a. major axis It is a line segment whose endpoints are the vertices , contains the foci and vertex and have
length of 2a units.
b. minor axis It is a line segment whose endpoints are the vertices B and B’ and have length of 2b units.
c. Foci It is denoted by C and C’ and have length of 2c units.
d. latera recta It is a line segment through the foci perpendicular to major axis and it is
𝑏2
𝑎
away from the
foci and whose endpoints are denoted by LR1 , LR2, LR3 and LR4.
e. directrix It is a line perpendicular to major axis and
𝑎2
𝑐
away from the center and it is denoted by D and
D’ .
f. center (C) It is the midway of the foci.
12.
13.
14. Parameters of Parabola
If a and b are the lengths of major and minor axis, then the distance of
the center to the focus, denoted by c, may be obtained from the equation
a2 = b2 + c2, where a>b and a>c
